The correct answer is option 3, Visakhapatnam. INS Tihayu, a fast attack craft, was commissioned by the Indian Navy in October 2016. It is important to note that a fast attack craft is a small, highly maneuverable warship designed to operate close to shorelines. INS Tihayu would be based in Visakhapatnam, which is a major naval base and headquarters for the Eastern Naval Command of the Indian Navy.

Option 1, Kochi, is incorrect because INS Tihayu is not based there. Kochi is another prominent naval base in India, but it is not the correct base for INS Tihayu.

Option 2, Panaji, is also incorrect. Panaji is the capital city of the Indian state of Goa, but it is not the intended base for INS Tihayu.

Option 4, Mumbai, is incorrect as well. Mumbai is the home of the Western Naval Command of the Indian Navy, but it is not the designated base for INS Tihayu.

In summary, the highly maneuverable fast attack craft INS Tihayu is based in Visakhapatnam, which is a crucial naval base for the Indian Navy.